Stable Klingen Vectors and Paramodular Newforms
Stable Klingen Vectors and Paramodular Newforms
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稳定的克林根向量和拟模新形式
DOI：
10.1007/978-3-031-45177-5
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发表时间：
2023
影响因子：
--
通讯作者：
Ralf Schmidt
中科院分区：
文献类型：
--
作者：
Jennifer Johnson;B. Roberts;Ralf Schmidt
本书描述了一种研究具有副模水平的二阶西格尔模形式的新颖方法。它引入了 GSp (4) 的稳定克林根同余子群族，并使用该族获得了拟模新形式的 Hecke 特征值和傅里叶系数之间的新关系，揭示了拟模表示的基本二分法。除其他重要结果外，它还包括对非阿基米德局部域上 GSp (4) 的所有不可约表示中这些同余子群固定的向量的完整描述。西格尔副模形式与自守表示理论和朗兰兹纲领、伽罗瓦表示、阿贝尔曲面算术和算法数论有联系。本书提供了有关该主题的有用标准资源，将引起从事上述领域工作的研究生和研究人员的兴趣。
This book describes a novel approach to the study of Siegel modular forms of degree two with paramodular level. It introduces the family of stable Klingen congruence subgroups of GSp (4) and uses this family to obtain new relations between the Hecke eigenvalues and Fourier coefficients of paramodular newforms, revealing a fundamental dichotomy for paramodular representations. Among other important results, it includes a complete description of the vectors fixed by these congruence subgroups in all irreducible representations of GSp (4) over a nonarchimedean local field. Siegel paramodular forms have connections with the theory of automorphic representations and the Langlands program, Galois representations, the arithmetic of abelian surfaces, and algorithmic number theory. Providing a useful standard source on the subject, the book will be of interest to graduate students and researchers working in the above fields.